Let us briefly refer to the related approaches for agents' pricing of differentiated goods under discrete choice demand. This has been studied in the context of
the oligopolistic price competition. Here, suppliers maximize their expected profits by setting prices and facing the discrete choice demand of consumers. We recommend [1]} for a basic overview. A central challenge of this approach is to induce analytical properties of the suppliers' profit function. Concavity of the expected revenue under the multinomial logit has been shown in [2]}, where the authors assume identical price sensitivities. This assumption is relaxed in [3]}. Furthermore, the authors prove concavity for the nested logit expected revenue functions, if the price sensitivities are equal for alternatives within the same nest. The concavity of the expected revenue functions is with respect to the market shares. Note that the multinomial logit expected revenue function is not concave with respect to prices [4]}.
